Generalized two dimensional fourier-laplace transform and topological properties

Due to wide spread applicability in integral transform for partial differential equations involving distributional conditions, many of integral transform extended to generalized function and in last few years, the theory of generalized integral transforms have been of ever increasing interest due to its application in physics especially in quantum field theory, engineering and pure as well as applied mathematics. It provided new aspect to many mathematical disciplines such as ordinary and partial differential equation, operational calculus transformation theory and functional analysis.

This paper presents the generalization of two dimensional Fourier-Laplace transform in the distributional sense. The testing function spaces using Gelfand-Shilov techniques are defined. Also some topological properties of S-type spaces for distributional generalized two dimensional Fourier-Laplace transform are proved.